Notations :
Standard Hours for actual output = SH
Standard Rate per hour = SR
Actual hours = AH
Actual Rate per hour = AR
Standard direct labour cost for actual output = SH * SR
Now.
Direct Labour Rate variance = (SR - AR) * AH --------------------Eq 1
$1800 (A) = (SR * AH) - (AR* AH)
(-) $1800 = (SR * AH) - Actual cost
(-) $1800 = (SR * AH) - $67000
(SR * AH) = $65200
SR = 65200 / AH
Direct labour efficiency variance = ( SH -AH) * SR ---------------------Eq 2
$2900 (F) = (SH * SR) - (AH * SR)
2900 = (SH * SR) - [ AH * ( 65200 / AH) ] ----------{from eq 1}
2900 = (SH * SR) - [65200]
(SH * SR) = 65200 + 2900
Standard direct labour cost for actual output = $68100
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